Pattern avoidance is an important topic in combinatorics on words which dates back to the
beginning of the twentieth century when Thue constructed an infinite word over a ternary
alphabet that avoids squares, i.e., a word with no two adjacent identical
factors. This result finds applications in various algebraic contexts where more general
patterns than squares are considered. On the other hand, Erdős raised the question as to
whether there exists an infinite word that avoids abelian squares, i.e.,
a word with no two adjacent factors being permutations of one another. Although this
question was answered affirmately years later, knowledge of abelian pattern avoidance is
rather limited. Recently, (abelian) pattern avoidance was initiated in the more general
framework of partial words, which allow for undefined positions called holes. In this
paper, we show that any pattern p with n> 3 distinct variables of
length at least 2n is abelian avoidable by a partial word
with infinitely many holes, the bound on the length of p being tight. We complete
the classification of all the binary and ternary patterns with respect to non-trivial
abelian avoidability, in which no variable can be substituted by only one hole. We also
investigate the abelian avoidability indices of the binary and ternary patterns.